OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (19 - 37*x + 20*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
From Amiram Eldar, Nov 03 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(19)*Pi*coth(sqrt(19)*Pi))/38.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(19)*Pi*cosech(sqrt(19)*Pi))/38. (End)
MAPLE
MATHEMATICA
Table[n^2 + 19, {n, 0, 60}]
LinearRecurrence[{3, -3, 1}, {19, 20, 23}, 50] (* Harvey P. Dale, Dec 05 2018 *)
PROG
(Magma) [n^2+19: n in [0..60]];
(PARI) a(n)=n^2+19 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 01 2014
STATUS
approved